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Title
Branching process models of cancer [electronic resource] / Richard Durrett.
ISBN
9783319160658 electronic book
3319160656 electronic book
9783319160641
Published
Cham : Springer, [2015]
Copyright
©2015
Language
English
Description
1 online resource (vii, 63 pages) : illustrations.
Item Number
10.1007/978-3-319-16065-8 doi
Call Number
RC267
Dewey Decimal Classification
616.99/40015118
Summary
This volume develops results on continuous time branching processes and applies them to study rate of tumor growth, extending classic work on the Luria-Delbruck distribution. As a consequence, the authors calculate the probability that mutations that confer resistance to treatment are present at detection and quantify the extent of tumor heterogeneity. As applications, the authors evaluate ovarian cancer screening strategies and give rigorous proofs for results of Heano and Michor concerning tumor metastasis. These notes should be accessible to students who are familiar with Poisson processes and continuous time. Richard Durrett is mathematics professor at Duke University, USA. He is the author of 8 books, over 200 journal articles, and has supervised more than 40 Ph.D. students. Most of his current research concerns the applications of probability to biology: ecology, genetics, and most recently cancer.
Bibliography, etc. Note
Includes bibliographical references.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed June 24, 2015).
Series
Mathematical Biosciences Institute lecture series. Stochastics in biological systems ; volume 1.
Available in Other Form
Print version: 9783319160641
Multistage Theory of Cancer
Mathematical Overview
Branching Process Results
Time for Z_0 to Reach Size M
Time Until the First Type 1
Mutation Before Detection?
Accumulation of Neutral Mutations
Properties of the Gamma Function
Growth of Z_1(t)
Movements of Z_1(t)
Luria-Delbruck Distributions
Number of Type 1's at Time T_M
Gwoth of Z_k(t)
Transitions Between Waves
Time to the First Type \tau_k, k \ge 2
Application: Metastasis
Application: Ovarian Cancer
Application: Intratumor Heterogeneity.
